GWR
2024-04-05
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## All packages loaded successfullyproject_directory <- dirname(getwd())Loading Data
Toronto Map
# load in the geojson of Toronto
toronto_geojson_file <- file.path(project_directory, "data", "geodata", "neighbourhoods.geojson")
toronto <- st_read(toronto_geojson_file)## Reading layer `neighbourhoods' from data source
## `/Users/michelleuni/Documents/UU/Spatial_Analysis/Term Project/data/geodata/neighbourhoods.geojson'
## using driver `GeoJSON'
## Simple feature collection with 140 features and 11 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -79.63926 ymin: 43.581 xmax: -79.11527 ymax: 43.85546
## Geodetic CRS: WGS 84# the AREA_NAME is the name of the neighbourhood
# we need to clean the text so it is the same as all the other files
toronto$AREA_NAME <- tolower(trimws(gsub("\\(\\d+\\)", "", toronto$AREA_NAME)))
toronto$AREA_NAME <- gsub("\\(\\d+\\)", "", toronto$AREA_NAME)
toronto$AREA_NAME <- gsub("[[:punct:]]", "", toronto$AREA_NAME)
names(toronto)[names(toronto) == "AREA_NAME"] <- "neighbourhood"
toronto$neighbourhood[which(toronto$neighbourhood == 'cabbagetownsouth stjames town')] <- 'cabbagetownsouth st james town'
toronto$neighbourhood[which(toronto$neighbourhood == 'north stjames town')] <- 'north st james town'
toronto <- toronto[order(toronto$neighbourhood), ]toronto$neighbourhood## [1] "agincourt north" "agincourt southmalvern west"
## [3] "alderwood" "annex"
## [5] "banburydon mills" "bathurst manor"
## [7] "bay street corridor" "bayview village"
## [9] "bayview woodssteeles" "bedford parknortown"
## [11] "beechboroughgreenbrook" "bendale"
## [13] "birchcliffecliffside" "black creek"
## [15] "blakejones" "briar hillbelgravia"
## [17] "bridle pathsunnybrookyork mills" "broadview north"
## [19] "brookhavenamesbury" "cabbagetownsouth st james town"
## [21] "caledoniafairbank" "casa loma"
## [23] "centennial scarborough" "churchyonge corridor"
## [25] "clairleabirchmount" "clanton park"
## [27] "cliffcrest" "corso italiadavenport"
## [29] "danforth" "danforth east york"
## [31] "don valley village" "dorset park"
## [33] "dovercourtwallace emersonjunction" "downsviewrodingcfb"
## [35] "dufferin grove" "east enddanforth"
## [37] "edenbridgehumber valley" "eglinton east"
## [39] "elmsold rexdale" "englemountlawrence"
## [41] "eringatecentennialwest deane" "etobicoke west mall"
## [43] "flemingdon park" "forest hill north"
## [45] "forest hill south" "glenfieldjane heights"
## [47] "greenwoodcoxwell" "guildwood"
## [49] "henry farm" "high park north"
## [51] "high parkswansea" "highland creek"
## [53] "hillcrest village" "humber heightswestmount"
## [55] "humber summit" "humbermede"
## [57] "humewoodcedarvale" "ionview"
## [59] "islingtoncity centre west" "junction area"
## [61] "keelesdaleeglinton west" "kennedy park"
## [63] "kensingtonchinatown" "kingsview villagethe westway"
## [65] "kingsway south" "lambton baby point"
## [67] "lamoreaux" "lansingwestgate"
## [69] "lawrence park north" "lawrence park south"
## [71] "leasidebennington" "little portugal"
## [73] "long branch" "malvern"
## [75] "maple leaf" "markland wood"
## [77] "milliken" "mimico includes humber bay shores"
## [79] "morningside" "moss park"
## [81] "mount dennis" "mount olivesilverstonejamestown"
## [83] "mount pleasant east" "mount pleasant west"
## [85] "new toronto" "newtonbrook east"
## [87] "newtonbrook west" "niagara"
## [89] "north riverdale" "north st james town"
## [91] "oakridge" "oakwood village"
## [93] "oconnorparkview" "old east york"
## [95] "palmerstonlittle italy" "parkwoodsdonalda"
## [97] "pelmo parkhumberlea" "playter estatesdanforth"
## [99] "pleasant view" "princessrosethorn"
## [101] "regent park" "rexdalekipling"
## [103] "rockcliffesmythe" "roncesvalles"
## [105] "rosedalemoore park" "rouge"
## [107] "runnymedebloor west village" "rustic"
## [109] "scarborough village" "south parkdale"
## [111] "south riverdale" "standrewwindfields"
## [113] "steeles" "stonegatequeensway"
## [115] "tam oshantersullivan" "taylormassey"
## [117] "the beaches" "thistletownbeaumond heights"
## [119] "thorncliffe park" "trinitybellwoods"
## [121] "university" "victoria village"
## [123] "waterfront communitiesthe island" "west hill"
## [125] "west humberclairville" "westminsterbranson"
## [127] "weston" "westonpelham park"
## [129] "wexfordmaryvale" "willowdale east"
## [131] "willowdale west" "willowridgemartingroverichview"
## [133] "woburn" "woodbine corridor"
## [135] "woodbinelumsden" "wychwood"
## [137] "yongeeglinton" "yongestclair"
## [139] "york university heights" "yorkdaleglen park"toronto_map <- ggplot() +
geom_sf(data = toronto, fill = "lightblue") +
theme_void()
toronto_map
Census 2016
The census files contain 63 variables that will be used as indicators.
# 2011
#census_path <- file.path(project_directory, "data", "census2011.csv")
#census <- read.csv(census_path, row.names = 1)
# 2016
census_path <- file.path(project_directory, "data", "census2016.csv")
census <- read.csv(census_path, row.names = 1)
census <- census[order(census$neighbourhood), ]
# 2021
#census_path <- file.path(project_directory, "data", "census2021.csv")
#census <- read.csv(census_path, row.names = 1)names(census)## [1] "neighbourhood" "single_detached_house"
## [3] "apart_5_plus" "other_dwelling"
## [5] "avg_household_size" "married"
## [7] "not_married" "single_parents"
## [9] "one_person_household" "two_plus_person_household"
## [11] "low_income_percent" "non_immigrants"
## [13] "immigrants" "owner"
## [15] "renter" "own_room"
## [17] "sharing_room" "suitable_housing"
## [19] "not_suitable_housing" "total_work_activity"
## [21] "unemployed" "employed"
## [23] "commute_drives" "commute_passenger"
## [25] "commute_public_transport" "commute_walk"
## [27] "commute_cycle" "commute_other"
## [29] "pop_0_to_4" "pop_5_to_9"
## [31] "pop_10_to_14" "pop_15_to_19"
## [33] "pop_20_to_24" "pop_25_to_29"
## [35] "pop_30_to_34" "pop_35_to_39"
## [37] "pop_40_to_44" "pop_45_to_49"
## [39] "pop_50_to_54" "pop_55_to_59"
## [41] "pop_60_to_64" "pop_65_to_69"
## [43] "pop_70_to_74" "pop_75_to_79"
## [45] "pop_80_to_84" "pop_85_to_89"
## [47] "pop_90_to_94" "pop_95_to_99"
## [49] "pop_100_plus" "household_income"
## [51] "income_under_5000" "income_between_5000_9999"
## [53] "income_between_10000_14999" "income_between_50000_59999"
## [55] "income_above_100k" "income_between_15000_19999"
## [57] "income_between_20000_29999" "income_between_30000_39999"
## [59] "income_between_40000_49999" "income_between_60000_79999"
## [61] "income_between_80000_99999" "no_certificate_diploma_degree"
## [63] "highschool_diploma" "post_secondary_diploma"
## [65] "total_population" "num_crimes"Add Population Density
# compute the area of each neighbourhood
toronto$area <- st_area(toronto)# calculate the popualtion density
census$population_density <- census$total_population/toronto$areaAdd Toronto Geometries to Census 2016
Currently, the census file only has the name of the neighbourhoods but no geometries. We need to add the geometries from toronto.geojson to the census file to perform the analysis.
census_with_geom <- merge(census, toronto, by.x = "neighbourhood", by.y = "neighbourhood", all.x = TRUE)
census_sf <- st_as_sf(census_with_geom)
st_crs(census_sf) <- st_crs(toronto)Add Parks
# load in the geojson of parks in Toronto
parks_geojson_file <- file.path(project_directory, "data", "geodata", "parks.geojson")
parks <- st_read(parks_geojson_file)## Reading layer `parks' from data source
## `/Users/michelleuni/Documents/UU/Spatial_Analysis/Term Project/data/geodata/parks.geojson'
## using driver `GeoJSON'
## Simple feature collection with 1702 features and 82 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -79.62752 ymin: 43.581 xmax: -79.1242 ymax: 43.84753
## Geodetic CRS: WGS 84names(parks)[names(parks) == "AREA_NAME"] <- "neighbourhood"
parks <- parks[order(parks$neighbourhood), ]# cleaning the neighbourhood names
parks$neighbourhood <- tolower(parks$neighbourhood)
parks$neighbourhood <- gsub("[[:punct:]0-9]", "", parks$neighbourhood)# Group the parks by neighbourhood
parks <- parks %>%
group_by(neighbourhood)
# Calculate the area of each park
parks <- parks %>%
mutate(park_area = st_area(geometry))
# Sum the area per neighbourhood
parks <- parks %>%
group_by(neighbourhood) %>%
summarise(total_park_area = sum(park_area))
# Add the neighbourhood area
parks <- parks %>%
mutate(neighbourhood_area = toronto$area)
# Calculate how much of the neighbourhood is a park
parks <- parks %>%
mutate(proportion = total_park_area/neighbourhood_area)# Order by neighbourhoods and add to the census file
parks <- parks[order(parks$neighbourhood), ]
census_sf <- census_sf %>%
mutate(proportion_park_area = parks$proportion)
census_sf$proportion_park_area <- as.numeric(census_sf$proportion_park_area)Add Libraries
# load in the geojson of libraries in Toronto
libraries_geojson_file <- file.path(project_directory, "data", "geodata", "libraries.geojson")
libraries<- st_read(libraries_geojson_file)## Reading layer `libraries' from data source
## `/Users/michelleuni/Documents/UU/Spatial_Analysis/Term Project/data/geodata/libraries.geojson'
## using driver `GeoJSON'
## Simple feature collection with 108 features and 63 fields
## Geometry type: MULTIPOINT
## Dimension: XY
## Bounding box: xmin: -79.61925 ymin: 43.59905 xmax: -79.14005 ymax: 43.82411
## Geodetic CRS: WGS 84names(libraries)[names(libraries) == "AREA_NAME"] <- "neighbourhood"
libraries <- libraries[order(libraries$neighbourhood), ]# data cleaning
libraries$neighbourhood <- tolower(libraries$neighbourhood)
libraries$neighbourhood <- gsub("[[:punct:]0-9]", "", libraries$neighbourhood)
libraries$neighbourhood <- trimws(libraries$neighbourhood)
libraries$neighbourhood[which(libraries$neighbourhood == 'cabbagetownsouth stjames town')] <- 'cabbagetownsouth st james town'
libraries$neighbourhood[which(libraries$neighbourhood == 'north stjames town')] <- 'north st james town'# group by neighbourhood to sum up number of libraries in each
libraries <- libraries %>%
group_by(neighbourhood) %>%
summarise(num_libraries = n())# some neighbourhoods have no libraries, but we still need them in the data
missing_neighborhoods <- setdiff(toronto$neighbourhood, libraries$neighbourhood)
length(missing_neighborhoods)## [1] 77toronto_missing <- toronto[toronto$neighbourhood %in% missing_neighborhoods, ]
toronto_missing <- subset(toronto, neighbourhood %in% missing_neighborhoods, select = c("neighbourhood", "geometry"))
toronto_missing$num_libraries <- 0# add the missing neighbourhoods
libraries <- rbind(libraries, toronto_missing)# order by neighbourhood and add to census
libraries <- libraries[order(libraries$neighbourhood), ]
census_sf <- census_sf %>%
mutate(num_libraries = libraries$num_libraries)Add Police Facilities
# load in the geojson of police facilities in Toronto
police_geojson_file <- file.path(project_directory, "data", "geodata", "distance_to_police.geojson")
police <- st_read(police_geojson_file)## Reading layer `distance_to_police' from data source
## `/Users/michelleuni/Documents/UU/Spatial_Analysis/Term Project/data/geodata/distance_to_police.geojson'
## using driver `GeoJSON'
## Simple feature collection with 140 features and 13 fields
## Geometry type: LINESTRING
## Dimension: XY
## Bounding box: xmin: -79.59636 ymin: 43.59236 xmax: -79.15084 ymax: 43.8212
## Geodetic CRS: WGS 84names(police)[names(police) == "AREA_NAME"] <- "neighbourhood"
police <- police[order(police$neighbourhood), ]# clean text
police$neighbourhood <- tolower(police$neighbourhood)
police$neighbourhood <- gsub("[[:punct:]0-9]", "", police$neighbourhood)
police$neighbourhood <- trimws(police$neighbourhood)# order by neighbourhood and add to census
police <- police[order(police$neighbourhood), ]
census_sf <- census_sf %>%
mutate(closest_police_facility = police$HubDist)This shows the closest police facility for every neighbourhood (measured in km).
# Overlay libraries
police_plot <- toronto_map +
geom_sf(data = police, color = "yellow", size = 1) +
theme_void()
# Print the map
print(police_plot)
Add Subway Stops
# load in the geojson of subway stops in Toronto
subway_geojson_file <- file.path(project_directory, "data", "geodata", "subway_stops.geojson")
subway <- st_read(subway_geojson_file)## Reading layer `subway_stops' from data source
## `/Users/michelleuni/Documents/UU/Spatial_Analysis/Term Project/data/geodata/subway_stops.geojson'
## using driver `GeoJSON'
## Simple feature collection with 614 features and 37 fields
## Geometry type: MULTIPOINT
## Dimension: XY
## Bounding box: xmin: -79.53769 ymin: 43.63569 xmax: -79.26372 ymax: 43.78225
## Geodetic CRS: WGS 84names(subway)[names(subway) == "AREA_NAME"] <- "neighbourhood"# clean text
subway$neighbourhood <- tolower(subway$neighbourhood)
subway$neighbourhood <- gsub("[[:punct:]0-9]", "", subway$neighbourhood)
subway$neighbourhood <- trimws(subway$neighbourhood)subway$neighbourhood[which(subway$neighbourhood == 'cabbagetownsouth stjames town')] <- 'cabbagetownsouth st james town'
subway$neighbourhood[which(subway$neighbourhood == 'north stjames town')] <- 'north st james town'# group by neighbourhood to sum up number of stops in each
subway <- subway %>%
group_by(neighbourhood) %>%
summarise(num_subway_stops = n())# some neighbourhoods have no stops, but we still need them in the data
missing_neighborhoods2 <- setdiff(toronto$neighbourhood, subway$neighbourhood)
toronto_missing2 <- toronto[toronto$neighbourhood %in% missing_neighborhoods2, ]
toronto_missing2 <- subset(toronto, neighbourhood %in% missing_neighborhoods2, select = c("neighbourhood", "geometry"))
toronto_missing2$num_subway_stops <- 0# add the missing neighbourhoods
subway <- rbind(subway, toronto_missing2)
subway <- subway[order(subway$neighbourhood), ]# add to census
census_sf <- census_sf %>%
mutate(num_subway_stops = subway$num_subway_stops)Add Red Light Cameras
# load in the geojson of Red light cameras in Toronto
cam_geojson_file <- file.path(project_directory, "data", "geodata", "cam2016.csv")
cameras <- read.csv(cam_geojson_file)
cameras <- cameras[order(cameras$neighbourhood), ]# clean neighbourhood text
cameras$neighbourhood[which(cameras$neighbourhood == 'cabbagetownsouth stjames town')] <- 'cabbagetownsouth st james town'
cameras$neighbourhood[which(cameras$neighbourhood == 'north stjames town')] <- 'north st james town'# add geometries to cameras data
subset_toronto <- toronto %>%
filter(neighbourhood %in% cameras$neighbourhood)
cameras <- cameras %>%
mutate(geometry = subset_toronto$geometry)# some neighbourhoods have no stops, but we still need them in the data
missing_neighborhoods3 <- setdiff(toronto$neighbourhood, cameras$neighbourhood)
toronto_missing3 <- toronto[toronto$neighbourhood %in% missing_neighborhoods3, ]
toronto_missing3 <- subset(toronto, neighbourhood %in% missing_neighborhoods3, select = c("neighbourhood"))
toronto_missing3$num_cameras <- 0# add the neighbourhoods with no cameras to the data
cameras <- cameras[order(cameras$neighbourhood), ]
cameras <- rbind(cameras, toronto_missing3)# add the camera data to census
census_sf <- census_sf %>%
mutate(num_cameras = cameras$num_cameras)Exploratory Spatial Data Analysis
# change fill to see different maps
ggplot() +
geom_sf(data = census_sf, aes(fill = num_crimes)) +
scale_fill_gradient(name = "Number of crimes", low = "grey", high = "red") +
theme_minimal()
Spatial Autocorrelation of Dependent Variable
#Continuity
crimedata_nbq <- poly2nb(census_sf, queen=TRUE)
crimedata_nbq_w <- nb2listw(crimedata_nbq, style="W", zero.policy = TRUE) #Queen’s
coordsW <- census_sf%>%
st_centroid()%>%
st_geometry()## Warning: st_centroid assumes attributes are constant over geometries#KNN
#crimedata_KNN <- knearneigh(coordsW, k=4)
#crimedata_nbq_KNN <- knn2nb(crimedata_KNN, sym=T)
#crimedata_KNN_w <- nb2listw(crimedata_nbq_KNN, style="W", zero.policy = TRUE)
plot(crimedata_nbq, st_geometry(coordsW), col="red")
mc_global <- moran.mc(census_sf$num_crimes, crimedata_nbq_w, 2999, alternative="greater")
#plot the Moran’s I
plot(mc_global)
mc_global##
## Monte-Carlo simulation of Moran I
##
## data: census_sf$num_crimes
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.34892, observed rank = 3000, p-value = 0.0003333
## alternative hypothesis: greaterFunctions for analysis
Linear Regression
#calculation
linear_regression_analysis <- function(equation, data) {
linearMod <- lm(equation, data = data)
summary_info <- summary(linearMod)
mc_global_OLS <- moran.mc(linearMod$residuals, crimedata_nbq_w, 2999, zero.policy = TRUE, alternative = "greater")
vif_values <- vif(linearMod)
# Save results
linear_results <- list(model = linearMod, summary = summary_info, vif = vif_values, moran=mc_global_OLS)
return(linear_results)
}plot_residuals <- function(linear_results){
qtm(residuals(linear_results$linearMod))
}LISA
# calculation
lisa_analysis <- function(data) {
gm_crime_LISA <- localmoran(data$num_crimes, crimedata_nbq_w)
summary_info <- summary(gm_crime_LISA)
# Save results
lisa_results <- list(gm_crime_LISA = gm_crime_LISA, summary = summary_info)
return(lisa_results)
}# visualisation
visualise_LISA <- function(data, gm_crime_LISA) {
sf_object <- data
sf_object$gm_crime_LISA <- gm_crime_LISA[, 1]
p_values <- gm_crime_LISA[, 5]
map_LISA <- tm_shape(sf_object) +
tm_polygons(col = "gm_crime_LISA", title = "Local Moran’s I", midpoint = 0,
palette = "RdYlBu", breaks = c(-1, -0.5, 0, 0.5, 1, 2))
map_LISA_p <- tm_shape(sf_object) +
tm_polygons(col = "gm_crime_LISA", title = "p-values",
breaks = c(0, 0.01, 0.05, 1), palette = "Reds")
tmap_arrange(map_LISA, map_LISA_p)
}# crime clusters
visualize_LISA_clusters <- function(data_sf, LISA_data, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan')) {
# Calculate mean value of the variable under consideration
meanVal <- mean(data_sf$num_crimes)
# Create a copy of LISA data to preserve original results
LISA_type <- LISA_data
# Create a tibble object storing the LISA values into different classes of significance
LISA_mapping <- LISA_type %>%
tibble::as_tibble() %>%
magrittr::set_colnames(c("Ii", "E.Ii", "Var.Ii", "Z.Ii", "Pr(z > 0)")) %>%
dplyr::mutate(coType = dplyr::case_when(
`Pr(z > 0)` > significanceLevel ~ "Insignificant", # Greater than significance level, thus Insignificant
`Pr(z > 0)` <= significanceLevel & Ii >= 0 & data_sf$num_crimes >= meanVal ~ "HH", # High-High local Moran's I values
`Pr(z > 0)` <= significanceLevel & Ii >= 0 & data_sf$num_crimes < meanVal ~ "LL", # Low-Low local Moran's I values
`Pr(z > 0)` <= significanceLevel & Ii < 0 & data_sf$num_crimes >= meanVal ~ "HL", # High-Low local Moran's I values
`Pr(z > 0)` <= significanceLevel & Ii < 0 & data_sf$num_crimes < meanVal ~ "LH" # Low-High local Moran's I values
))
# Join back to the main polygon data
data_sf$coType <- LISA_mapping$coType %>% tidyr::replace_na("Insignificant")
# Map the clusters
ggplot(data_sf) +
geom_sf(aes(fill = coType)) +
scale_fill_manual(values = colors, name = 'Clusters & \nOutliers') +
labs(title = "Crime clusters") +
theme(panel.background = element_rect(fill = 'transparent'))
}GWR
# calculation
gwr_analysis <- function(equation, data, i) {
crimedata_sp <- as_Spatial(data)
print(paste("---Equation", i, "---"))
abw <- bw.gwr(equation, approach = "AIC", adaptive = TRUE, kernel = "gaussian", data = crimedata_sp)
a.gwr <- gwr.basic(equation, adaptive = TRUE, kernel = "gaussian", bw = abw, data = crimedata_sp)
# Save results
gwr_results <- list(a.gwr = a.gwr)
return(gwr_results)
}# visualisation
extract_predictors <- function(equation) {
predictors <- attr(terms(equation), "term.labels")
return(predictors)
}
visualise_gwr <- function(agwr_sf, equation) {
predictors <- extract_predictors(equation)
maps <- lapply(predictors, function(predictor) {
qtm_map <- qtm(agwr_sf, predictor)
return(qtm_map)
})
tmap_arrange(maps, asp = 5, ncol = 1)
}Processing
Equations
# only social indicators
eq1 <- num_crimes ~ unemployed + household_income + no_certificate_diploma_degree + commute_walk
eq2 <- num_crimes ~ unemployed + household_income + no_certificate_diploma_degree + commute_public_transport
eq3 <- num_crimes ~ commute_public_transport + income_under_5000 + immigrants + pop_15_to_19 + no_certificate_diploma_degree
# only physical indicators - change these to include Asha's physical indicators
eq4 <- num_crimes ~ num_cameras + proportion_park_area + closest_police_facility
eq5 <- num_crimes ~ population_density + proportion_park_area + closest_police_facility + num_subway_stops
eq6 <- num_crimes ~ proportion_park_area + closest_police_facility + num_cameras
# both social and physical indicators
eq7 <- num_crimes ~ unemployed + + commute_public_transport + population_density + proportion_park_area
eq8 <- num_crimes ~ household_income + no_certificate_diploma_degree + num_cameras + population_density
eq9 <- num_crimes ~ low_income_percent + population_density + num_subway_stops + no_certificate_diploma_degree
eq10 <- num_crimes ~ proportion_park_area + unemployed + population_density + no_certificate_diploma_degree + household_income
# List of equations
equations <- list(eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10)Calculations
linear_results_list <- list()
lisa_results_list <- list()
gwr_results_list <- list()
# Perform analysis for each equation
for (i in seq_along(equations)) {
eq <- equations[[i]]
# Linear Regression Analysis
linear_results_list[[i]] <- linear_regression_analysis(eq, census_sf)
# LISA Analysis
lisa_results_list[[i]] <- lisa_analysis(census_sf)
# GWR Analysis
gwr_results_list[[i]] <- gwr_analysis(eq, census_sf, i)
}## [1] "---Equation 1 ---"
## Adaptive bandwidth (number of nearest neighbours): 94 AICc value: 1760.241
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1756.92
## Adaptive bandwidth (number of nearest neighbours): 48 AICc value: 1753.423
## Adaptive bandwidth (number of nearest neighbours): 37 AICc value: 1750.522
## Adaptive bandwidth (number of nearest neighbours): 30 AICc value: 1748.303
## Adaptive bandwidth (number of nearest neighbours): 26 AICc value: 1747.261
## Adaptive bandwidth (number of nearest neighbours): 23 AICc value: 1746.78
## Adaptive bandwidth (number of nearest neighbours): 21 AICc value: 1746.737
## Adaptive bandwidth (number of nearest neighbours): 20 AICc value: 1747.365
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1746.459
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1746.459
## [1] "---Equation 2 ---"
## Adaptive bandwidth (number of nearest neighbours): 94 AICc value: 1783.573
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1780.546
## Adaptive bandwidth (number of nearest neighbours): 48 AICc value: 1776.387
## Adaptive bandwidth (number of nearest neighbours): 37 AICc value: 1772.109
## Adaptive bandwidth (number of nearest neighbours): 30 AICc value: 1767.095
## Adaptive bandwidth (number of nearest neighbours): 26 AICc value: 1764.025
## Adaptive bandwidth (number of nearest neighbours): 23 AICc value: 1762.681
## Adaptive bandwidth (number of nearest neighbours): 21 AICc value: 1762.711
## Adaptive bandwidth (number of nearest neighbours): 24 AICc value: 1763.131
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1762.553
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1762.553
## [1] "---Equation 3 ---"
## Adaptive bandwidth (number of nearest neighbours): 94 AICc value: 1787.52
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1783.18
## Adaptive bandwidth (number of nearest neighbours): 48 AICc value: 1777.206
## Adaptive bandwidth (number of nearest neighbours): 37 AICc value: 1772.909
## Adaptive bandwidth (number of nearest neighbours): 30 AICc value: 1768.506
## Adaptive bandwidth (number of nearest neighbours): 26 AICc value: 1765.848
## Adaptive bandwidth (number of nearest neighbours): 23 AICc value: 1764.928
## Adaptive bandwidth (number of nearest neighbours): 21 AICc value: 1764.499
## Adaptive bandwidth (number of nearest neighbours): 20 AICc value: 1764.748
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1764.432
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1764.432
## [1] "---Equation 4 ---"
## Adaptive bandwidth (number of nearest neighbours): 94 AICc value: 1904.455
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1903.733
## Adaptive bandwidth (number of nearest neighbours): 48 AICc value: 1900.686
## Adaptive bandwidth (number of nearest neighbours): 37 AICc value: 1897.09
## Adaptive bandwidth (number of nearest neighbours): 30 AICc value: 1894.362
## Adaptive bandwidth (number of nearest neighbours): 26 AICc value: 1892.383
## Adaptive bandwidth (number of nearest neighbours): 23 AICc value: 1891.444
## Adaptive bandwidth (number of nearest neighbours): 21 AICc value: 1891.096
## Adaptive bandwidth (number of nearest neighbours): 20 AICc value: 1891.498
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1891.047
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1891.047
## [1] "---Equation 5 ---"
## Adaptive bandwidth (number of nearest neighbours): 94 AICc value: 1857.355
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1856.905
## Adaptive bandwidth (number of nearest neighbours): 48 AICc value: 1855.55
## Adaptive bandwidth (number of nearest neighbours): 37 AICc value: 1854.73
## Adaptive bandwidth (number of nearest neighbours): 30 AICc value: 1853.745
## Adaptive bandwidth (number of nearest neighbours): 26 AICc value: 1853.508
## Adaptive bandwidth (number of nearest neighbours): 23 AICc value: 1853.501
## Adaptive bandwidth (number of nearest neighbours): 21 AICc value: 1853.679
## Adaptive bandwidth (number of nearest neighbours): 24 AICc value: 1853.7
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1853.185
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1853.185
## [1] "---Equation 6 ---"
## Adaptive bandwidth (number of nearest neighbours): 94 AICc value: 1904.455
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1903.733
## Adaptive bandwidth (number of nearest neighbours): 48 AICc value: 1900.686
## Adaptive bandwidth (number of nearest neighbours): 37 AICc value: 1897.09
## Adaptive bandwidth (number of nearest neighbours): 30 AICc value: 1894.362
## Adaptive bandwidth (number of nearest neighbours): 26 AICc value: 1892.383
## Adaptive bandwidth (number of nearest neighbours): 23 AICc value: 1891.444
## Adaptive bandwidth (number of nearest neighbours): 21 AICc value: 1891.096
## Adaptive bandwidth (number of nearest neighbours): 20 AICc value: 1891.498
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1891.047
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1891.047
## [1] "---Equation 7 ---"
## Adaptive bandwidth (number of nearest neighbours): 94 AICc value: 1824.117
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1819.372
## Adaptive bandwidth (number of nearest neighbours): 48 AICc value: 1813.101
## Adaptive bandwidth (number of nearest neighbours): 37 AICc value: 1806.292
## Adaptive bandwidth (number of nearest neighbours): 30 AICc value: 1799.875
## Adaptive bandwidth (number of nearest neighbours): 26 AICc value: 1794.906
## Adaptive bandwidth (number of nearest neighbours): 23 AICc value: 1791.349
## Adaptive bandwidth (number of nearest neighbours): 21 AICc value: 1788.752
## Adaptive bandwidth (number of nearest neighbours): 20 AICc value: 1787.138
## Adaptive bandwidth (number of nearest neighbours): 19 AICc value: 1784.808
## Adaptive bandwidth (number of nearest neighbours): 19 AICc value: 1784.808
## [1] "---Equation 8 ---"
## Adaptive bandwidth (number of nearest neighbours): 94 AICc value: 1784.154
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1781.083
## Adaptive bandwidth (number of nearest neighbours): 48 AICc value: 1777.658
## Adaptive bandwidth (number of nearest neighbours): 37 AICc value: 1775.712
## Adaptive bandwidth (number of nearest neighbours): 30 AICc value: 1773.202
## Adaptive bandwidth (number of nearest neighbours): 26 AICc value: 1771.712
## Adaptive bandwidth (number of nearest neighbours): 23 AICc value: 1770.57
## Adaptive bandwidth (number of nearest neighbours): 21 AICc value: 1770.53
## Adaptive bandwidth (number of nearest neighbours): 20 AICc value: 1770.348
## Adaptive bandwidth (number of nearest neighbours): 19 AICc value: 1769.09
## Adaptive bandwidth (number of nearest neighbours): 19 AICc value: 1769.09
## [1] "---Equation 9 ---"
## Adaptive bandwidth (number of nearest neighbours): 94 AICc value: 1840.426
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1839.856
## Adaptive bandwidth (number of nearest neighbours): 48 AICc value: 1838.918
## Adaptive bandwidth (number of nearest neighbours): 37 AICc value: 1838.712
## Adaptive bandwidth (number of nearest neighbours): 30 AICc value: 1838.271
## Adaptive bandwidth (number of nearest neighbours): 26 AICc value: 1838.123
## Adaptive bandwidth (number of nearest neighbours): 23 AICc value: 1838.247
## Adaptive bandwidth (number of nearest neighbours): 27 AICc value: 1838.167
## Adaptive bandwidth (number of nearest neighbours): 24 AICc value: 1838.087
## Adaptive bandwidth (number of nearest neighbours): 24 AICc value: 1838.087
## [1] "---Equation 10 ---"
## Adaptive bandwidth (number of nearest neighbours): 94 AICc value: 1779.979
## Adaptive bandwidth (number of nearest neighbours): 66 AICc value: 1776.633
## Adaptive bandwidth (number of nearest neighbours): 48 AICc value: 1772.516
## Adaptive bandwidth (number of nearest neighbours): 37 AICc value: 1768.819
## Adaptive bandwidth (number of nearest neighbours): 30 AICc value: 1765.395
## Adaptive bandwidth (number of nearest neighbours): 26 AICc value: 1763.111
## Adaptive bandwidth (number of nearest neighbours): 23 AICc value: 1762.292
## Adaptive bandwidth (number of nearest neighbours): 21 AICc value: 1762.3
## Adaptive bandwidth (number of nearest neighbours): 24 AICc value: 1762.521
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1761.99
## Adaptive bandwidth (number of nearest neighbours): 22 AICc value: 1761.99Linear Regression Plots
# equation 1
linear_results_list[[1]]## $model
##
## Call:
## lm(formula = equation, data = data)
##
## Coefficients:
## (Intercept) unemployed
## 15.435032 -0.002092
## household_income no_certificate_diploma_degree
## 0.012563 0.037000
## commute_walk
## 0.057229
##
##
## $summary
##
## Call:
## lm(formula = equation, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -433.27 -55.99 -16.01 25.81 717.82
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 15.435032 25.374382 0.608 0.544016
## unemployed -0.002092 0.009019 -0.232 0.816917
## household_income 0.012563 0.006286 1.999 0.047651 *
## no_certificate_diploma_degree 0.037000 0.010403 3.557 0.000519 ***
## commute_walk 0.057229 0.010883 5.259 5.54e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 129.5 on 135 degrees of freedom
## Multiple R-squared: 0.6571, Adjusted R-squared: 0.6469
## F-statistic: 64.67 on 4 and 135 DF, p-value: < 2.2e-16
##
##
## $vif
## unemployed household_income
## 6.880903 7.525150
## no_certificate_diploma_degree commute_walk
## 3.171722 3.880383
##
## $moran
##
## Monte-Carlo simulation of Moran I
##
## data: linearMod$residuals
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.076061, observed rank = 2863, p-value = 0.04567
## alternative hypothesis: greater# equation 2
linear_results_list[[2]]## $model
##
## Call:
## lm(formula = equation, data = data)
##
## Coefficients:
## (Intercept) unemployed
## -21.52553 -0.02597
## household_income no_certificate_diploma_degree
## 0.05018 0.04327
## commute_public_transport
## -0.03021
##
##
## $summary
##
## Call:
## lm(formula = equation, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -309.39 -59.17 -22.17 27.73 743.16
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -21.525534 26.117903 -0.824 0.411298
## unemployed -0.025968 0.008486 -3.060 0.002670 **
## household_income 0.050176 0.006080 8.253 1.24e-13 ***
## no_certificate_diploma_degree 0.043272 0.011463 3.775 0.000239 ***
## commute_public_transport -0.030208 0.014509 -2.082 0.039234 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 140 on 135 degrees of freedom
## Multiple R-squared: 0.5997, Adjusted R-squared: 0.5878
## F-statistic: 50.56 on 4 and 135 DF, p-value: < 2.2e-16
##
##
## $vif
## unemployed household_income
## 5.218472 6.030366
## no_certificate_diploma_degree commute_public_transport
## 3.298805 5.143706
##
## $moran
##
## Monte-Carlo simulation of Moran I
##
## data: linearMod$residuals
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.18061, observed rank = 2996, p-value = 0.001333
## alternative hypothesis: greater# equation 3
linear_results_list[[3]]## $model
##
## Call:
## lm(formula = equation, data = data)
##
## Coefficients:
## (Intercept) commute_public_transport
## -1.495e+01 3.785e-02
## income_under_5000 immigrants
## 4.134e-01 -1.527e-02
## pop_15_to_19 no_certificate_diploma_degree
## -2.255e-06 6.690e-02
##
##
## $summary
##
## Call:
## lm(formula = equation, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -557.55 -55.20 -9.46 25.68 831.67
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.495e+01 2.918e+01 -0.513 0.609127
## commute_public_transport 3.785e-02 1.029e-02 3.680 0.000337 ***
## income_under_5000 4.134e-01 5.385e-02 7.678 3.02e-12 ***
## immigrants -1.527e-02 4.826e-03 -3.164 0.001928 **
## pop_15_to_19 -2.255e-06 5.207e-06 -0.433 0.665720
## no_certificate_diploma_degree 6.690e-02 1.268e-02 5.277 5.15e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 143.5 on 134 degrees of freedom
## Multiple R-squared: 0.582, Adjusted R-squared: 0.5664
## F-statistic: 37.32 on 5 and 134 DF, p-value: < 2.2e-16
##
##
## $vif
## commute_public_transport income_under_5000
## 2.457894 2.196649
## immigrants pop_15_to_19
## 5.926523 2.193423
## no_certificate_diploma_degree
## 3.835492
##
## $moran
##
## Monte-Carlo simulation of Moran I
##
## data: linearMod$residuals
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.19566, observed rank = 2999, p-value = 0.0003333
## alternative hypothesis: greater# equation 4
linear_results_list[[4]]## $model
##
## Call:
## lm(formula = equation, data = data)
##
## Coefficients:
## (Intercept) num_cameras proportion_park_area
## 367.832 -4.988 -256.239
## closest_police_facility
## -39.488
##
##
## $summary
##
## Call:
## lm(formula = equation, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -232.04 -127.14 -53.54 40.88 1040.75
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 367.832 42.919 8.570 2.01e-14 ***
## num_cameras -4.988 12.918 -0.386 0.70000
## proportion_park_area -256.239 215.370 -1.190 0.23621
## closest_police_facility -39.488 14.355 -2.751 0.00676 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 212.4 on 136 degrees of freedom
## Multiple R-squared: 0.07146, Adjusted R-squared: 0.05098
## F-statistic: 3.489 on 3 and 136 DF, p-value: 0.01757
##
##
## $vif
## num_cameras proportion_park_area closest_police_facility
## 1.012933 1.037584 1.028877
##
## $moran
##
## Monte-Carlo simulation of Moran I
##
## data: linearMod$residuals
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.33258, observed rank = 3000, p-value = 0.0003333
## alternative hypothesis: greater# equation 5
linear_results_list[[5]]## $model
##
## Call:
## lm(formula = equation, data = data)
##
## Coefficients:
## (Intercept) population_density proportion_park_area
## 198.752 9.584 -14.275
## closest_police_facility num_subway_stops
## -14.284 1.812
##
##
## $summary
##
## Call:
## lm(formula = equation, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -550.21 -87.32 -36.26 56.68 922.38
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 198.752 40.865 4.864 3.16e-06 ***
## population_density 9.584 1.334 7.182 4.18e-11 ***
## proportion_park_area -14.275 185.389 -0.077 0.939
## closest_police_facility -14.284 12.631 -1.131 0.260
## num_subway_stops 1.812 1.177 1.540 0.126
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 179.7 on 135 degrees of freedom
## Multiple R-squared: 0.34, Adjusted R-squared: 0.3204
## F-statistic: 17.39 on 4 and 135 DF, p-value: 1.579e-11
##
##
## $vif
## population_density proportion_park_area closest_police_facility
## 1.123477 1.073673 1.112365
## num_subway_stops
## 1.032180
##
## $moran
##
## Monte-Carlo simulation of Moran I
##
## data: linearMod$residuals
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.19558, observed rank = 3000, p-value = 0.0003333
## alternative hypothesis: greater# equation 6
linear_results_list[[6]]## $model
##
## Call:
## lm(formula = equation, data = data)
##
## Coefficients:
## (Intercept) proportion_park_area closest_police_facility
## 367.832 -256.239 -39.488
## num_cameras
## -4.988
##
##
## $summary
##
## Call:
## lm(formula = equation, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -232.04 -127.14 -53.54 40.88 1040.75
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 367.832 42.919 8.570 2.01e-14 ***
## proportion_park_area -256.239 215.370 -1.190 0.23621
## closest_police_facility -39.488 14.355 -2.751 0.00676 **
## num_cameras -4.988 12.918 -0.386 0.70000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 212.4 on 136 degrees of freedom
## Multiple R-squared: 0.07146, Adjusted R-squared: 0.05098
## F-statistic: 3.489 on 3 and 136 DF, p-value: 0.01757
##
##
## $vif
## proportion_park_area closest_police_facility num_cameras
## 1.037584 1.028877 1.012933
##
## $moran
##
## Monte-Carlo simulation of Moran I
##
## data: linearMod$residuals
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.33258, observed rank = 3000, p-value = 0.0003333
## alternative hypothesis: greater# equation 7
linear_results_list[[7]]## $model
##
## Call:
## lm(formula = equation, data = data)
##
## Coefficients:
## (Intercept) unemployed commute_public_transport
## 26.83523 0.01141 0.03689
## population_density proportion_park_area
## 5.39234 -70.31357
##
##
## $summary
##
## Call:
## lm(formula = equation, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -430.52 -66.64 -22.01 25.82 814.00
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 26.835225 37.207572 0.721 0.472015
## unemployed 0.011410 0.005957 1.915 0.057544 .
## commute_public_transport 0.036894 0.012524 2.946 0.003795 **
## population_density 5.392337 1.524416 3.537 0.000555 ***
## proportion_park_area -70.313569 166.291306 -0.423 0.673089
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 163.9 on 135 degrees of freedom
## Multiple R-squared: 0.4508, Adjusted R-squared: 0.4346
## F-statistic: 27.71 on 4 and 135 DF, p-value: < 2.2e-16
##
##
## $vif
## unemployed commute_public_transport population_density
## 1.874388 2.793738 1.761982
## proportion_park_area
## 1.038220
##
## $moran
##
## Monte-Carlo simulation of Moran I
##
## data: linearMod$residuals
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.29882, observed rank = 3000, p-value = 0.0003333
## alternative hypothesis: greater# equation 8
linear_results_list[[8]]## $model
##
## Call:
## lm(formula = equation, data = data)
##
## Coefficients:
## (Intercept) household_income
## -19.82803 0.02625
## no_certificate_diploma_degree num_cameras
## 0.01469 -8.85584
## population_density
## 3.64098
##
##
## $summary
##
## Call:
## lm(formula = equation, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -406.07 -52.73 -14.07 30.77 748.92
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -19.828030 27.215403 -0.729 0.46753
## household_income 0.026250 0.003344 7.851 1.14e-12 ***
## no_certificate_diploma_degree 0.014688 0.006988 2.102 0.03741 *
## num_cameras -8.855844 8.794282 -1.007 0.31574
## population_density 3.640975 1.255088 2.901 0.00434 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 142 on 135 degrees of freedom
## Multiple R-squared: 0.5879, Adjusted R-squared: 0.5757
## F-statistic: 48.16 on 4 and 135 DF, p-value: < 2.2e-16
##
##
## $vif
## household_income no_certificate_diploma_degree
## 1.771998 1.191055
## num_cameras population_density
## 1.050118 1.591810
##
## $moran
##
## Monte-Carlo simulation of Moran I
##
## data: linearMod$residuals
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.22648, observed rank = 3000, p-value = 0.0003333
## alternative hypothesis: greater# equation 9
linear_results_list[[9]]## $model
##
## Call:
## lm(formula = equation, data = data)
##
## Coefficients:
## (Intercept) low_income_percent
## 45.55742 2.31358
## population_density num_subway_stops
## 8.94888 2.12519
## no_certificate_diploma_degree
## 0.02907
##
##
## $summary
##
## Call:
## lm(formula = equation, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -510.91 -68.76 -16.35 29.98 980.26
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 45.557423 40.309422 1.130 0.260399
## low_income_percent 2.313579 1.981853 1.167 0.245114
## population_density 8.948876 1.252485 7.145 5.09e-11 ***
## num_subway_stops 2.125189 1.098550 1.935 0.055138 .
## no_certificate_diploma_degree 0.029068 0.008018 3.625 0.000408 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 169.6 on 135 degrees of freedom
## Multiple R-squared: 0.4118, Adjusted R-squared: 0.3944
## F-statistic: 23.63 on 4 and 135 DF, p-value: 7.975e-15
##
##
## $vif
## low_income_percent population_density
## 1.181203 1.110509
## num_subway_stops no_certificate_diploma_degree
## 1.009740 1.098619
##
## $moran
##
## Monte-Carlo simulation of Moran I
##
## data: linearMod$residuals
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.19267, observed rank = 3000, p-value = 0.0003333
## alternative hypothesis: greater# equation 10
linear_results_list[[10]]## $model
##
## Call:
## lm(formula = equation, data = data)
##
## Coefficients:
## (Intercept) proportion_park_area
## -9.02102 -93.41696
## unemployed population_density
## -0.02447 3.32138
## no_certificate_diploma_degree household_income
## 0.03905 0.03447
##
##
## $summary
##
## Call:
## lm(formula = equation, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -344.93 -53.85 -15.00 28.11 730.09
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.021021 30.412083 -0.297 0.767211
## proportion_park_area -93.416965 140.333806 -0.666 0.506762
## unemployed -0.024474 0.008401 -2.913 0.004195 **
## population_density 3.321381 1.237831 2.683 0.008211 **
## no_certificate_diploma_degree 0.039047 0.011129 3.509 0.000614 ***
## household_income 0.034469 0.004207 8.194 1.78e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 138.4 on 134 degrees of freedom
## Multiple R-squared: 0.6113, Adjusted R-squared: 0.5968
## F-statistic: 42.15 on 5 and 134 DF, p-value: < 2.2e-16
##
##
## $vif
## proportion_park_area unemployed
## 1.036856 5.228300
## population_density no_certificate_diploma_degree
## 1.629149 3.178776
## household_income
## 2.951207
##
## $moran
##
## Monte-Carlo simulation of Moran I
##
## data: linearMod$residuals
## weights: crimedata_nbq_w
## number of simulations + 1: 3000
##
## statistic = 0.18295, observed rank = 2999, p-value = 0.0003333
## alternative hypothesis: greatercensus_sf$residuals1 <- residuals(linear_results_list[[1]]$model)
census_sf$residuals2 <- residuals(linear_results_list[[2]]$model)
census_sf$residuals3 <- residuals(linear_results_list[[3]]$model)
census_sf$residuals4 <- residuals(linear_results_list[[4]]$model)
census_sf$residuals5 <- residuals(linear_results_list[[5]]$model)
qtm(census_sf, "residuals1")## Variable(s) "residuals1" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
qtm(census_sf, "residuals2")## Variable(s) "residuals2" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
qtm(census_sf, "residuals3")## Variable(s) "residuals3" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
qtm(census_sf, "residuals4")## Variable(s) "residuals4" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
qtm(census_sf, "residuals5")## Variable(s) "residuals5" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
census_sf$residuals6 <- residuals(linear_results_list[[6]]$model)
census_sf$residuals7 <- residuals(linear_results_list[[7]]$model)
census_sf$residuals8 <- residuals(linear_results_list[[8]]$model)
census_sf$residuals9 <- residuals(linear_results_list[[9]]$model)
census_sf$residuals10 <- residuals(linear_results_list[[10]]$model)
qtm(census_sf, "residuals6")## Variable(s) "residuals6" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
qtm(census_sf, "residuals7")## Variable(s) "residuals7" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
qtm(census_sf, "residuals8")## Variable(s) "residuals8" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
qtm(census_sf, "residuals9")## Variable(s) "residuals9" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
qtm(census_sf, "residuals10")## Variable(s) "residuals10" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
LISA Plots
visualise_LISA(census_sf, lisa_results_list[[1]]$gm_crime_LISA)## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
visualise_LISA(census_sf, lisa_results_list[[2]]$gm_crime_LISA)## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
visualise_LISA(census_sf, lisa_results_list[[3]]$gm_crime_LISA)## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
visualise_LISA(census_sf, lisa_results_list[[4]]$gm_crime_LISA)## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
visualise_LISA(census_sf, lisa_results_list[[5]]$gm_crime_LISA)## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
visualise_LISA(census_sf, lisa_results_list[[6]]$gm_crime_LISA)## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
visualise_LISA(census_sf, lisa_results_list[[7]]$gm_crime_LISA)## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
visualise_LISA(census_sf, lisa_results_list[[8]]$gm_crime_LISA)## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
visualise_LISA(census_sf, lisa_results_list[[9]]$gm_crime_LISA)## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
visualise_LISA(census_sf, lisa_results_list[[10]]$gm_crime_LISA)## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
## Warning: Values have found that are higher than the highest break## Warning: Values have found that are less than the lowest break## Warning: Values have found that are higher than the highest break
visualize_LISA_clusters(census_sf, lisa_results_list[[1]]$gm_crime_LISA, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan'))
visualize_LISA_clusters(census_sf, lisa_results_list[[2]]$gm_crime_LISA, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan'))
visualize_LISA_clusters(census_sf, lisa_results_list[[3]]$gm_crime_LISA, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan'))
visualize_LISA_clusters(census_sf, lisa_results_list[[4]]$gm_crime_LISA, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan'))
visualize_LISA_clusters(census_sf, lisa_results_list[[5]]$gm_crime_LISA, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan'))
visualize_LISA_clusters(census_sf, lisa_results_list[[6]]$gm_crime_LISA, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan'))
visualize_LISA_clusters(census_sf, lisa_results_list[[7]]$gm_crime_LISA, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan'))
visualize_LISA_clusters(census_sf, lisa_results_list[[8]]$gm_crime_LISA, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan'))
visualize_LISA_clusters(census_sf, lisa_results_list[[9]]$gm_crime_LISA, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan'))
visualize_LISA_clusters(census_sf, lisa_results_list[[10]]$gm_crime_LISA, significanceLevel = 0.05, colors = c('red', 'brown', 'NA', 'blue', 'cyan'))
GWR Plots
# Plot first 5 GWR results for each equation
for (i in seq_along(gwr_results_list[1:5])) {
gwr_result <- gwr_results_list[[i]]
equation <- equations[[i]]
# Extract GWR spatial data frame
agwr_sf <- st_as_sf(gwr_result$a.gwr$SDF)
# Visualize GWR result
gwr_plot <- visualise_gwr(agwr_sf, equation)
# Print GWR plot
print(gwr_plot)
}## Variable(s) "unemployed" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "household_income" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "no_certificate_diploma_degree" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
## Variable(s) "unemployed" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
## Variable(s) "no_certificate_diploma_degree" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "commute_public_transport" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
## Variable(s) "immigrants" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "pop_15_to_19" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
## Variable(s) "num_cameras" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "proportion_park_area" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "closest_police_facility" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
## Variable(s) "proportion_park_area" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
## Variable(s) "closest_police_facility" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "num_subway_stops" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
for (i in seq_along(gwr_results_list)[6:10]) {
gwr_result <- gwr_results_list[[i]]
equation <- equations[[i]]
# Extract GWR spatial data frame
agwr_sf <- st_as_sf(gwr_result$a.gwr$SDF)
# Visualize GWR result
gwr_plot <- visualise_gwr(agwr_sf, equation)
# Print GWR plot
print(gwr_plot)
}## Variable(s) "proportion_park_area" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "closest_police_facility" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "num_cameras" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
## Variable(s) "commute_public_transport" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "population_density" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "proportion_park_area" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
## Variable(s) "no_certificate_diploma_degree" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "num_cameras" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "population_density" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
## Variable(s) "low_income_percent" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
## Variable(s) "proportion_park_area" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "unemployed" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "population_density" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Variable(s) "no_certificate_diploma_degree" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
for (i in seq_along(gwr_results_list)[1:10]) {
print(paste("---Equation", i, "---"))
gwr_result <- gwr_results_list[[i]]
print(gwr_result)
}## [1] "---Equation 1 ---"
## $a.gwr
## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2024-04-07 17:15:47.001221
## Call:
## gwr.basic(formula = equation, data = crimedata_sp, bw = abw,
## kernel = "gaussian", adaptive = TRUE)
##
## Dependent (y) variable: num_crimes
## Independent variables: unemployed household_income no_certificate_diploma_degree commute_walk
## Number of data points: 140
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -433.27 -55.99 -16.01 25.81 717.82
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 15.435032 25.374382 0.608 0.544016
## unemployed -0.002092 0.009019 -0.232 0.816917
## household_income 0.012563 0.006286 1.999 0.047651 *
## no_certificate_diploma_degree 0.037000 0.010403 3.557 0.000519 ***
## commute_walk 0.057229 0.010883 5.259 5.54e-07 ***
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 129.5 on 135 degrees of freedom
## Multiple R-squared: 0.6571
## Adjusted R-squared: 0.6469
## F-statistic: 64.67 on 4 and 135 DF, p-value: < 2.2e-16
## ***Extra Diagnostic information
## Residual sum of squares: 2265108
## Sigma(hat): 128.1165
## AIC: 1766.111
## AICc: 1766.743
## BIC: 1673.411
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Adaptive bandwidth: 22 (number of nearest neighbours)
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median
## Intercept -6.1624e+01 -3.4597e+01 1.4617e+01
## unemployed -2.0279e-02 -3.7619e-03 1.7803e-02
## household_income -1.0063e-02 4.1355e-04 5.6404e-03
## no_certificate_diploma_degree -1.5108e-02 6.0329e-03 2.5839e-02
## commute_walk 4.9848e-02 6.4015e-02 6.8297e-02
## 3rd Qu. Max.
## Intercept 3.5492e+01 58.5950
## unemployed 3.4307e-02 0.0725
## household_income 1.0614e-02 0.0252
## no_certificate_diploma_degree 3.5214e-02 0.0488
## commute_walk 7.4259e-02 0.0869
## ************************Diagnostic information*************************
## Number of data points: 140
## Effective number of parameters (2trace(S) - trace(S'S)): 18.61278
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 121.3872
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1746.459
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1726.534
## BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 1641.855
## Residual sum of squares: 1682682
## R-square value: 0.7452506
## Adjusted R-square value: 0.7058644
##
## ***********************************************************************
## Program stops at: 2024-04-07 17:15:47.014301
##
## [1] "---Equation 2 ---"
## $a.gwr
## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2024-04-07 17:15:47.288642
## Call:
## gwr.basic(formula = equation, data = crimedata_sp, bw = abw,
## kernel = "gaussian", adaptive = TRUE)
##
## Dependent (y) variable: num_crimes
## Independent variables: unemployed household_income no_certificate_diploma_degree commute_public_transport
## Number of data points: 140
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -309.39 -59.17 -22.17 27.73 743.16
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -21.525534 26.117903 -0.824 0.411298
## unemployed -0.025968 0.008486 -3.060 0.002670 **
## household_income 0.050176 0.006080 8.253 1.24e-13 ***
## no_certificate_diploma_degree 0.043272 0.011463 3.775 0.000239 ***
## commute_public_transport -0.030208 0.014509 -2.082 0.039234 *
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 140 on 135 degrees of freedom
## Multiple R-squared: 0.5997
## Adjusted R-squared: 0.5878
## F-statistic: 50.56 on 4 and 135 DF, p-value: < 2.2e-16
## ***Extra Diagnostic information
## Residual sum of squares: 2644201
## Sigma(hat): 138.4228
## AIC: 1787.776
## AICc: 1788.408
## BIC: 1695.076
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Adaptive bandwidth: 22 (number of nearest neighbours)
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median
## Intercept -73.8348478 -59.0694103 -26.8243959
## unemployed -0.0424779 -0.0341738 -0.0093677
## household_income 0.0090013 0.0394579 0.0504573
## no_certificate_diploma_degree -0.0015523 0.0204869 0.0344750
## commute_public_transport -0.0762816 -0.0546858 -0.0272557
## 3rd Qu. Max.
## Intercept -11.3151128 8.3486
## unemployed 0.0058134 0.0484
## household_income 0.0551360 0.0680
## no_certificate_diploma_degree 0.0463477 0.0568
## commute_public_transport -0.0127525 0.0216
## ************************Diagnostic information*************************
## Number of data points: 140
## Effective number of parameters (2trace(S) - trace(S'S)): 19.72839
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 120.2716
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1762.553
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1741.559
## BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 1659.605
## Residual sum of squares: 1864086
## R-square value: 0.7177869
## Adjusted R-square value: 0.6711068
##
## ***********************************************************************
## Program stops at: 2024-04-07 17:15:47.29628
##
## [1] "---Equation 3 ---"
## $a.gwr
## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2024-04-07 17:15:47.560728
## Call:
## gwr.basic(formula = equation, data = crimedata_sp, bw = abw,
## kernel = "gaussian", adaptive = TRUE)
##
## Dependent (y) variable: num_crimes
## Independent variables: commute_public_transport income_under_5000 immigrants pop_15_to_19 no_certificate_diploma_degree
## Number of data points: 140
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -557.55 -55.20 -9.46 25.68 831.67
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.495e+01 2.918e+01 -0.513 0.609127
## commute_public_transport 3.785e-02 1.029e-02 3.680 0.000337 ***
## income_under_5000 4.134e-01 5.385e-02 7.678 3.02e-12 ***
## immigrants -1.527e-02 4.826e-03 -3.164 0.001928 **
## pop_15_to_19 -2.255e-06 5.207e-06 -0.433 0.665720
## no_certificate_diploma_degree 6.690e-02 1.268e-02 5.277 5.15e-07 ***
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 143.5 on 134 degrees of freedom
## Multiple R-squared: 0.582
## Adjusted R-squared: 0.5664
## F-statistic: 37.32 on 5 and 134 DF, p-value: < 2.2e-16
## ***Extra Diagnostic information
## Residual sum of squares: 2760955
## Sigma(hat): 141.4458
## AIC: 1795.825
## AICc: 1796.674
## BIC: 1711.008
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Adaptive bandwidth: 22 (number of nearest neighbours)
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median
## Intercept -3.3218e+01 -1.8378e+01 -1.1973e+01
## commute_public_transport 7.9514e-03 1.8361e-02 2.9492e-02
## income_under_5000 2.5623e-01 3.3878e-01 4.0024e-01
## immigrants -1.8066e-02 -1.5364e-02 -7.6042e-03
## pop_15_to_19 -6.4194e-05 -1.9380e-05 -6.9424e-06
## no_certificate_diploma_degree 1.4210e-02 3.2091e-02 4.7701e-02
## 3rd Qu. Max.
## Intercept -1.4684e+00 18.0480
## commute_public_transport 4.4120e-02 0.0510
## income_under_5000 4.3367e-01 0.4686
## immigrants 2.3738e-03 0.0193
## pop_15_to_19 3.8098e-06 0.0000
## no_certificate_diploma_degree 6.3108e-02 0.0838
## ************************Diagnostic information*************************
## Number of data points: 140
## Effective number of parameters (2trace(S) - trace(S'S)): 22.61687
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 117.3831
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1764.432
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1739.39
## BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 1667.32
## Residual sum of squares: 1802856
## R-square value: 0.7270568
## Adjusted R-square value: 0.6740154
##
## ***********************************************************************
## Program stops at: 2024-04-07 17:15:47.568841
##
## [1] "---Equation 4 ---"
## $a.gwr
## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2024-04-07 17:15:47.810621
## Call:
## gwr.basic(formula = equation, data = crimedata_sp, bw = abw,
## kernel = "gaussian", adaptive = TRUE)
##
## Dependent (y) variable: num_crimes
## Independent variables: num_cameras proportion_park_area closest_police_facility
## Number of data points: 140
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -232.04 -127.14 -53.54 40.88 1040.75
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 367.832 42.919 8.570 2.01e-14 ***
## num_cameras -4.988 12.918 -0.386 0.70000
## proportion_park_area -256.239 215.370 -1.190 0.23621
## closest_police_facility -39.488 14.355 -2.751 0.00676 **
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 212.4 on 136 degrees of freedom
## Multiple R-squared: 0.07146
## Adjusted R-squared: 0.05098
## F-statistic: 3.489 on 3 and 136 DF, p-value: 0.01757
## ***Extra Diagnostic information
## Residual sum of squares: 6133221
## Sigma(hat): 210.8166
## AIC: 1903.565
## AICc: 1904.013
## BIC: 1802.982
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Adaptive bandwidth: 22 (number of nearest neighbours)
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median 3rd Qu. Max.
## Intercept 229.71277 311.97516 336.89196 391.94978 594.0225
## num_cameras -9.70079 -2.88659 0.55099 5.81046 20.5915
## proportion_park_area -408.35352 -283.57464 -197.98076 30.57308 823.1804
## closest_police_facility -192.21347 -88.90788 -34.55906 -25.08515 0.2925
## ************************Diagnostic information*************************
## Number of data points: 140
## Effective number of parameters (2trace(S) - trace(S'S)): 20.37017
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 119.6298
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1891.047
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1869.74
## BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 1788.573
## Residual sum of squares: 4650272
## R-square value: 0.2959726
## Adjusted R-square value: 0.1750826
##
## ***********************************************************************
## Program stops at: 2024-04-07 17:15:47.817415
##
## [1] "---Equation 5 ---"
## $a.gwr
## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2024-04-07 17:15:48.135646
## Call:
## gwr.basic(formula = equation, data = crimedata_sp, bw = abw,
## kernel = "gaussian", adaptive = TRUE)
##
## Dependent (y) variable: num_crimes
## Independent variables: population_density proportion_park_area closest_police_facility num_subway_stops
## Number of data points: 140
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -550.21 -87.32 -36.26 56.68 922.38
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 198.752 40.865 4.864 3.16e-06 ***
## population_density 9.584 1.334 7.182 4.18e-11 ***
## proportion_park_area -14.275 185.389 -0.077 0.939
## closest_police_facility -14.284 12.631 -1.131 0.260
## num_subway_stops 1.812 1.177 1.540 0.126
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 179.7 on 135 degrees of freedom
## Multiple R-squared: 0.34
## Adjusted R-squared: 0.3204
## F-statistic: 17.39 on 4 and 135 DF, p-value: 1.579e-11
## ***Extra Diagnostic information
## Residual sum of squares: 4359452
## Sigma(hat): 177.7364
## AIC: 1857.773
## AICc: 1858.404
## BIC: 1765.073
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Adaptive bandwidth: 22 (number of nearest neighbours)
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median 3rd Qu. Max.
## Intercept 134.44988 162.83182 198.24236 233.00653 299.5681
## population_density 7.26071 8.39807 9.27368 9.70532 10.3964
## proportion_park_area -242.96143 -85.21682 23.26152 234.32662 990.7974
## closest_police_facility -113.39043 -38.38879 -19.13964 -7.13310 2.7784
## num_subway_stops -0.78955 0.12342 2.23241 3.80642 5.0122
## ************************Diagnostic information*************************
## Number of data points: 140
## Effective number of parameters (2trace(S) - trace(S'S)): 21.65444
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 118.3456
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1853.185
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1829.922
## BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 1753.589
## Residual sum of squares: 3468614
## R-square value: 0.4748696
## Adjusted R-square value: 0.3779643
##
## ***********************************************************************
## Program stops at: 2024-04-07 17:15:48.144198
##
## [1] "---Equation 6 ---"
## $a.gwr
## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2024-04-07 17:15:48.391736
## Call:
## gwr.basic(formula = equation, data = crimedata_sp, bw = abw,
## kernel = "gaussian", adaptive = TRUE)
##
## Dependent (y) variable: num_crimes
## Independent variables: proportion_park_area closest_police_facility num_cameras
## Number of data points: 140
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -232.04 -127.14 -53.54 40.88 1040.75
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 367.832 42.919 8.570 2.01e-14 ***
## proportion_park_area -256.239 215.370 -1.190 0.23621
## closest_police_facility -39.488 14.355 -2.751 0.00676 **
## num_cameras -4.988 12.918 -0.386 0.70000
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 212.4 on 136 degrees of freedom
## Multiple R-squared: 0.07146
## Adjusted R-squared: 0.05098
## F-statistic: 3.489 on 3 and 136 DF, p-value: 0.01757
## ***Extra Diagnostic information
## Residual sum of squares: 6133221
## Sigma(hat): 210.8166
## AIC: 1903.565
## AICc: 1904.013
## BIC: 1802.982
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Adaptive bandwidth: 22 (number of nearest neighbours)
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median 3rd Qu. Max.
## Intercept 229.71277 311.97516 336.89196 391.94978 594.0225
## proportion_park_area -408.35352 -283.57464 -197.98076 30.57308 823.1804
## closest_police_facility -192.21347 -88.90788 -34.55906 -25.08515 0.2925
## num_cameras -9.70079 -2.88659 0.55099 5.81046 20.5915
## ************************Diagnostic information*************************
## Number of data points: 140
## Effective number of parameters (2trace(S) - trace(S'S)): 20.37017
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 119.6298
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1891.047
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1869.74
## BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 1788.573
## Residual sum of squares: 4650272
## R-square value: 0.2959726
## Adjusted R-square value: 0.1750826
##
## ***********************************************************************
## Program stops at: 2024-04-07 17:15:48.397787
##
## [1] "---Equation 7 ---"
## $a.gwr
## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2024-04-07 17:15:48.65317
## Call:
## gwr.basic(formula = equation, data = crimedata_sp, bw = abw,
## kernel = "gaussian", adaptive = TRUE)
##
## Dependent (y) variable: num_crimes
## Independent variables: unemployed commute_public_transport population_density proportion_park_area
## Number of data points: 140
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -430.52 -66.64 -22.01 25.82 814.00
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 26.835225 37.207572 0.721 0.472015
## unemployed 0.011410 0.005957 1.915 0.057544 .
## commute_public_transport 0.036894 0.012524 2.946 0.003795 **
## population_density 5.392337 1.524416 3.537 0.000555 ***
## proportion_park_area -70.313569 166.291306 -0.423 0.673089
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 163.9 on 135 degrees of freedom
## Multiple R-squared: 0.4508
## Adjusted R-squared: 0.4346
## F-statistic: 27.71 on 4 and 135 DF, p-value: < 2.2e-16
## ***Extra Diagnostic information
## Residual sum of squares: 3627337
## Sigma(hat): 162.1267
## AIC: 1832.034
## AICc: 1832.666
## BIC: 1739.334
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Adaptive bandwidth: 19 (number of nearest neighbours)
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median 3rd Qu.
## Intercept -1.3508e+02 -3.7114e+01 -1.0911e+01 4.2343e+01
## unemployed 1.6021e-03 5.6019e-03 3.8700e-02 4.6515e-02
## commute_public_transport -2.6135e-02 2.8722e-03 2.1210e-02 3.4285e-02
## population_density -5.3054e+00 3.6118e+00 5.6726e+00 6.8221e+00
## proportion_park_area -3.6726e+02 -1.5372e+02 -1.0836e+02 -4.2448e+01
## Max.
## Intercept 107.5167
## unemployed 0.0914
## commute_public_transport 0.0482
## population_density 7.7320
## proportion_park_area 106.2313
## ************************Diagnostic information*************************
## Number of data points: 140
## Effective number of parameters (2trace(S) - trace(S'S)): 24.71607
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 115.2839
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1784.808
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1758.129
## BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 1689.876
## Residual sum of squares: 2046852
## R-square value: 0.6901171
## Adjusted R-square value: 0.623099
##
## ***********************************************************************
## Program stops at: 2024-04-07 17:15:48.66252
##
## [1] "---Equation 8 ---"
## $a.gwr
## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2024-04-07 17:15:49.137439
## Call:
## gwr.basic(formula = equation, data = crimedata_sp, bw = abw,
## kernel = "gaussian", adaptive = TRUE)
##
## Dependent (y) variable: num_crimes
## Independent variables: household_income no_certificate_diploma_degree num_cameras population_density
## Number of data points: 140
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -406.07 -52.73 -14.07 30.77 748.92
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -19.828030 27.215403 -0.729 0.46753
## household_income 0.026250 0.003344 7.851 1.14e-12 ***
## no_certificate_diploma_degree 0.014688 0.006988 2.102 0.03741 *
## num_cameras -8.855844 8.794282 -1.007 0.31574
## population_density 3.640975 1.255088 2.901 0.00434 **
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 142 on 135 degrees of freedom
## Multiple R-squared: 0.5879
## Adjusted R-squared: 0.5757
## F-statistic: 48.16 on 4 and 135 DF, p-value: < 2.2e-16
## ***Extra Diagnostic information
## Residual sum of squares: 2721693
## Sigma(hat): 140.4365
## AIC: 1791.82
## AICc: 1792.451
## BIC: 1699.12
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Adaptive bandwidth: 19 (number of nearest neighbours)
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median
## Intercept -73.7991530 -44.1665266 -30.5708101
## household_income 0.0170042 0.0236128 0.0266122
## no_certificate_diploma_degree -0.0149289 -0.0030724 0.0046439
## num_cameras -17.1173816 -10.2604467 -5.5767477
## population_density -5.0847038 2.2122315 3.2628813
## 3rd Qu. Max.
## Intercept -1.0586464 29.8677
## household_income 0.0300324 0.0349
## no_certificate_diploma_degree 0.0307159 0.0483
## num_cameras 0.2476667 9.9414
## population_density 4.3169203 5.7759
## ************************Diagnostic information*************************
## Number of data points: 140
## Effective number of parameters (2trace(S) - trace(S'S)): 23.19567
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 116.8043
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1769.09
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1744.166
## BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 1671.817
## Residual sum of squares: 1866363
## R-square value: 0.7174422
## Adjusted R-square value: 0.6608458
##
## ***********************************************************************
## Program stops at: 2024-04-07 17:15:49.144344
##
## [1] "---Equation 9 ---"
## $a.gwr
## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2024-04-07 17:15:49.373388
## Call:
## gwr.basic(formula = equation, data = crimedata_sp, bw = abw,
## kernel = "gaussian", adaptive = TRUE)
##
## Dependent (y) variable: num_crimes
## Independent variables: low_income_percent population_density num_subway_stops no_certificate_diploma_degree
## Number of data points: 140
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -510.91 -68.76 -16.35 29.98 980.26
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 45.557423 40.309422 1.130 0.260399
## low_income_percent 2.313579 1.981853 1.167 0.245114
## population_density 8.948876 1.252485 7.145 5.09e-11 ***
## num_subway_stops 2.125189 1.098550 1.935 0.055138 .
## no_certificate_diploma_degree 0.029068 0.008018 3.625 0.000408 ***
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 169.6 on 135 degrees of freedom
## Multiple R-squared: 0.4118
## Adjusted R-squared: 0.3944
## F-statistic: 23.63 on 4 and 135 DF, p-value: 7.975e-15
## ***Extra Diagnostic information
## Residual sum of squares: 3885129
## Sigma(hat): 167.7889
## AIC: 1841.646
## AICc: 1842.278
## BIC: 1748.946
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Adaptive bandwidth: 24 (number of nearest neighbours)
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median
## Intercept -33.4928813 13.9610700 49.0743882
## low_income_percent -0.5706088 1.4261659 2.2099247
## population_density 4.7649903 7.4130685 8.3484725
## num_subway_stops 0.1403672 0.7470319 2.0993184
## no_certificate_diploma_degree 0.0075631 0.0170019 0.0206368
## 3rd Qu. Max.
## Intercept 77.7222912 105.0295
## low_income_percent 3.3855122 8.0519
## population_density 9.3195416 11.0161
## num_subway_stops 3.1885013 4.0570
## no_certificate_diploma_degree 0.0371097 0.0554
## ************************Diagnostic information*************************
## Number of data points: 140
## Effective number of parameters (2trace(S) - trace(S'S)): 18.92858
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 121.0714
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1838.087
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1817.737
## BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 1734.149
## Residual sum of squares: 3221543
## R-square value: 0.5122748
## Adjusted R-square value: 0.4353877
##
## ***********************************************************************
## Program stops at: 2024-04-07 17:15:49.380212
##
## [1] "---Equation 10 ---"
## $a.gwr
## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2024-04-07 17:15:49.629272
## Call:
## gwr.basic(formula = equation, data = crimedata_sp, bw = abw,
## kernel = "gaussian", adaptive = TRUE)
##
## Dependent (y) variable: num_crimes
## Independent variables: proportion_park_area unemployed population_density no_certificate_diploma_degree household_income
## Number of data points: 140
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -344.93 -53.85 -15.00 28.11 730.09
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.021021 30.412083 -0.297 0.767211
## proportion_park_area -93.416965 140.333806 -0.666 0.506762
## unemployed -0.024474 0.008401 -2.913 0.004195 **
## population_density 3.321381 1.237831 2.683 0.008211 **
## no_certificate_diploma_degree 0.039047 0.011129 3.509 0.000614 ***
## household_income 0.034469 0.004207 8.194 1.78e-13 ***
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 138.4 on 134 degrees of freedom
## Multiple R-squared: 0.6113
## Adjusted R-squared: 0.5968
## F-statistic: 42.15 on 5 and 134 DF, p-value: < 2.2e-16
## ***Extra Diagnostic information
## Residual sum of squares: 2567528
## Sigma(hat): 136.4012
## AIC: 1785.656
## AICc: 1786.505
## BIC: 1700.839
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Adaptive bandwidth: 22 (number of nearest neighbours)
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median
## Intercept -6.1334e+01 -4.1665e+01 -2.4132e+01
## proportion_park_area -2.9067e+02 -1.6617e+02 -1.1388e+02
## unemployed -4.0084e-02 -3.1607e-02 -6.4119e-03
## population_density -1.9072e+00 2.0861e+00 3.2772e+00
## no_certificate_diploma_degree -2.9914e-02 6.7411e-03 2.8945e-02
## household_income 1.5900e-02 2.2850e-02 3.1899e-02
## 3rd Qu. Max.
## Intercept -5.8560e+00 20.9199
## proportion_park_area -5.9940e+01 32.8675
## unemployed 1.2029e-02 0.0492
## population_density 4.0492e+00 5.2178
## no_certificate_diploma_degree 4.2281e-02 0.0531
## household_income 3.7936e-02 0.0425
## ************************Diagnostic information*************************
## Number of data points: 140
## Effective number of parameters (2trace(S) - trace(S'S)): 23.24892
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 116.7511
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1761.99
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1736.594
## BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 1665.357
## Residual sum of squares: 1764534
## R-square value: 0.7328585
## Adjusted R-square value: 0.6792024
##
## ***********************************************************************
## Program stops at: 2024-04-07 17:15:49.637444